Why do fireflies increase with number of samples when using a hdri light source?
Fireflies is just the name that we give to the bright, isolated, pixel that seems to create a color discontinuity with the pixel in the neigborhood.

It is said they are resulting


  ...from numerical instabilities in solving the rendering equation.


So, talking about the rendering algorithm


  there is no guarantee that it would converge to the correct solution


Despite this, I think that in your case (and most of the times) the method is able to give a good solution, it's just a matter of iterations number.

Below you can see a few steps of the rendering process and an ending comparison with the result achievable by enabling Multiple Importance samples (see Commonly Ignored Features #1 from the author of the HDRI)



So "fireflies" from this point of view, can be considered as just the earliest stage of the rendering process, as they are when rendering caustics. We consider them bad because compared with other parts of the scene the area where they appears is always behind in terms of convergence.

Stop killing the wonderful fireflies! :)